International Journal of Theoretical Physics

, Volume 45, Issue 4, pp 843–850 | Cite as

Reconstruction of Five-Dimensional Bounce Cosmological Models from Deceleration Factor

  • Lixin Xu
  • Hongya LiuEmail author
  • Yongli Ping


In this paper, we consider a class of five-dimensional Ricci-flat vacuum solutions, which contain two arbitrary functions μ(t) and ν(t). It is shown that μ(t) can be rewritten as a new arbitrary function f(z) in terms of redshift z and the f(z) can be determined by choosing particular deceleration parameters q(z) which gives early deceleration and late time acceleration. In this way, the 5D cosmological model can be reconstructed and the evolution of the universe can be determined.


Kaluza–Klein theory cosmology 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Anderson, E. (2004). The Campbell–Magaard Theorem is inadequate and inappropriate as a protective theorem for relativistic field equations, gr-qc/0409122.Google Scholar
  2. Armendáriz-Picón, Damour, T., and Mukhanov, V. (1999). k-Inflation. Physics Letters B 458, 209.CrossRefADSMathSciNetzbMATHGoogle Scholar
  3. Banerjee, N. and Das, S. (2005). Acceleration of the universe with a simple trigonometric potential, astro-ph/0505121.Google Scholar
  4. Barris, B. J., et al. (2004). 23 High Redshift Supernovae from the If A Deep Survey: Doubling the SN Sample at z > 0.7. Astrophysical Journal 602, 571, astro-ph/0310843.Google Scholar
  5. Caldwell, R. R., Kamionkowski, M., and Weinberg, N. N. (2003). Phantom Energy: Dark Energy with w > −1 Causes a Cosmic Doomsday. Physical Review Letter 91, 071301, astro-ph/0302506.Google Scholar
  6. Caldwell, R. R. (2002). A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state. Physical Letters B 545, 23, astro-ph/9908168.Google Scholar
  7. Chiba, T. (2002). Tracking k-essence. Physical Review D 66, 063514, astro-ph/0206298.Google Scholar
  8. Cooray, A. R. and Huterer, D. (1999). Astrophysics Journal 513, L95.CrossRefADSGoogle Scholar
  9. Dahia, F. and Romero, C. (2005). Dynamically generated embeddings of spacetime, gr-qc0503103.Google Scholar
  10. de Bernardis, P., et al. (2002). A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation. Nature 404, 955, astro-ph/0004404.Google Scholar
  11. Gerke, B. F. and Efstathiou, G. (2002). Monthly Notices Royal Astronomical Society 335, 33.CrossRefADSGoogle Scholar
  12. Guo, Z. K., Ohtab, N., and Zhang, Y. Z. (2005). Parametrization of Quintessence and Its Potential, astro-ph/0505253.Google Scholar
  13. Hanany, S., et al. (2000). MAXIMA-1: A Measurement of the Cosmic Microwave Background Anisotropy on angular scales of 10 arcminutes to 5 degrees. Astrophysical Journal 545, L5, astro-ph/0005123.Google Scholar
  14. Hannestad, S. and Mortsell, E. (2002). Physical Review D66, 063508.ADSGoogle Scholar
  15. Hao, J. G. and Li, X. Z. (2003). Attractor Solution of Phantom Field. Physical Review D 67, 107303, gr-qc/0302100.Google Scholar
  16. Kaluza, T. (1921). On The Problem Of Unity In Physics, Sitzungsber. Preuss. Akad. Wiss. Berlin (Mathematical Physics) K1966.Google Scholar
  17. Klein, O. (1926). Quantum Theory And Five-Dimensional Relativity. Zeitrchrist fur Physic 37, 895 [Surveys High Energering Physics 5 241 (1926)].Google Scholar
  18. Knop, R. A., et al. (2003). New Constraints on ΩM, ΩΛ, and w from an Independent Set of Eleven High-Redshift Supernovae Observed with HST, astro-ph/0309368.Google Scholar
  19. Liko, T. and Wesson, P. S. (2003). gr-qc/0310067.Google Scholar
  20. Linder, E. V. (2003). Physical Review Letter 90, 091301.CrossRefADSGoogle Scholar
  21. Liu, H. Y. (2003). Exact global solutions of brane universe and big bounce. Physical Letter B 560, 149, hep-th/0206198.Google Scholar
  22. Liu, H. Y. and Mashhoon, B. (1995). A machian interpretation of the cosmological constant. Annales Physics 4, 565.CrossRefADSzbMATHGoogle Scholar
  23. Liu, H. Y. and Wesson, P. S. (2001). Universe models with a variable cosmological “constant” and a “big bounce”. Astrophysical Journal 562, 1, gr-qc/0107093.Google Scholar
  24. Maartens, R. (2004). Brane-world gravity. Living Rev. Rel 7, 7, gr-qc/0312059.Google Scholar
  25. Malquarti, M., Copeland, E. J., Liddle, A. R., and Trodden, M. (2003). A new view of k-essence. Physical Review D 67, 123503.CrossRefADSMathSciNetGoogle Scholar
  26. Padmanabhan, T. and Choudhury, T. R. (2003). Monthly Notices Royal Astronomical Society 344, 823.CrossRefADSGoogle Scholar
  27. Perlmutter, S., et al. (1999). Measurements of omega and lambda from 42 high-redshift supernovae. Astrophysical Journal 517, 565, astro-ph/9812133.Google Scholar
  28. Ponce de Leon, J. (1988). General Relativity Gravity 20, 539.CrossRefADSMathSciNetGoogle Scholar
  29. Ponce de Leon, J. (1988). General Relativity Gravity 20 539.CrossRefADSMathSciNetGoogle Scholar
  30. Ponce de Leon, J. (2001). Modern Physics Letter A 16, 2291–2304, gr-qc/0111011.Google Scholar
  31. Riess, A. G., et al. (1998). Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astronomical Journal 116, 1009, astro-ph/9805201.Google Scholar
  32. Riess, A. G., et al. (2004). Type Ia Supernova Discoveries at z > 1 From the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution, astro-ph/0402512.Google Scholar
  33. Sahni, V. (2002). The cosmological constant problem and quintessence. Classical Quantum Gravity 19, 3435, astro-ph/0202076.Google Scholar
  34. Sahni, V. (2003). Theoretical models of dark energy. Chaos Solitan and Fractals 16 527.CrossRefzbMATHGoogle Scholar
  35. Seahra, S. S. and Wesson, P. S. (2003). Application of the Campbell-Magaard theorem to higher-dimensional physics. Classical and Quantum Gravity 20, 1321, gr-qc/0302015.Google Scholar
  36. Seahra, S. S. and Wesson, P. S. (2003). Universes encircling five-dimensional black holes. Journal of Mathematical Physics 44, 5664.CrossRefADSMathSciNetzbMATHGoogle Scholar
  37. Singh, P., Sami, M., and Dadhich, N. (2003). Cosmological dynamics of a phantom field. Physical Review D 68, 023522, hep-th/0305110.Google Scholar
  38. Spergel, D. N., et al. (2003). First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters. Astrophysical Journal Supplement 148, 175, astro-ph/0302209.Google Scholar
  39. Steinhardt, P. J., Wang, L., and Zlatev, I. (1999). Cosmological Tracking Solutions. Physical Review D 59, 123504, astro-ph/9812313.Google Scholar
  40. Tonry, J. L., et al. (2003). Cosmological Results from High-z Supernovae. Astrophysical Journal 594, 1, astro-ph/0305008.Google Scholar
  41. Turner, M. S. (2002). Making Sense of the New Cosmology. International Journal Modern Physics A 17S1, 180, astro-ph/0202008Google Scholar
  42. Wang, B. L., Liu, H. Y., and Xu, L. X. (2004). Accelerating Universe in a Big Bounce Model. Modern Physics Letter A 19, 449, gr-qc/0304093.Google Scholar
  43. Wesson, P. S. (1999). Space-Time-Matter (Singapore: World Scientific).Google Scholar
  44. Xu, L. X. and Liu, H. Y. (2006). The Correspondence Between a Five-dimensional Bounce cosmological Model and Quintessence Dark Energy Models. Modern Physics Letter A 21, 3105, astro-ph/0507397.Google Scholar
  45. Xu, L. X. and Liu, H. Y. (2005) Three Components Evolution in a Simple Big Bounce Cosmological Model, International Journal Modern Physics D 14, 883, astro-ph/0412241.Google Scholar
  46. Xu, L. X., Liu, H. Y., and Wang, B. L. (2003). Big Bounce singularity of a simple five-dimensional cosmological model. Chinease Physical Letter 20, 995, gr-qc/0304049.Google Scholar
  47. Zlatev, I., Wang, L., and Steinhardt, P. J. (1999). Quintessence, Cosmic Coincidence, and the Cosmological Constant. Physical Review Letter 82, 896, astro-ph/9807002.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of PhysicsDalian University of TechnologyDalianP. R. China

Personalised recommendations